Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
370 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#6226 | C2 | semidirect |
| 3. C3×C9×C4⋊C4 | C2 | semidirect |
| 6. #88534 | C2 | semidirect |
| 7. #88534 | C2 | semidirect |
| 28. C9×C4⋊C4 | D3 | semidirect |
| 36. C2×C3⋊D9 | Q8 | semidirect |
| 71. C3×C4⋊C4 | D9 | semidirect |
| 102. C3×C9 | C22⋊Q8 | semidirect |
| 133. C4⋊C4 | C3⋊D9 | semidirect |
| 157. C9 | #896 | semidirect |
| 185. C3 | #63458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D9 | 2 |
| C2×#6226 | 2 |
| C3×C9×C4⋊C4 | 2 |
| #88536 | 2 |
| #88534 | 2 |
| #64105 | 3 |
| #63458 | 3 |